Modeling of multilevel cell memory with the ${\mathrm{BaTiO}}_3/\mathrm{Fe}$ nanostructured multiferroic composite material

In order to enhance the performance of calculators, multilevel cell (MLC) memories have been proposed as an alternative solution to improve the communication speed between their processors and memories, and also in order to increase the effective storage density of memory devices. In this Rapid Communication, we propose a model of MLC memory based on a multiferroic (MF) composite material. We introduce a one-dimensional trilayer ferromagnetic/ferroelectric/ferromagnetic MF composite material through which we investigate theoretically the dynamics of an electromagnon excitation displaying a soliton structure with an envelope shape. It emerges from this study based on barium titanate (${\text{BaTiO}}_3$) and iron (Fe) that, for suitable values of the parameters of a single initial polarization excitation, some propagation scenarios display the encoding of the states of a system of two magnetic bits, i.e., the 11, 10, 01, and 00 states. In addition to this result, it is also realized that the system exhibits another scenario for which the signal propagating in the MF material is alternately converted from an electrical signal into a magnetic signal and reversely. Such outcomes suggest, on the one hand, the possibility to model a four-level MLC memory, and on the other hand, the modeling of an electromagnetic oscillator, based on a MF composite material.

Figure 1

A trilayer ferroelectric (orange) and ferromagnetic (blue) multiferroic composite material. As in the previous studies on the bilayer model, the trilayer MF material is discretized in a coarse-grained approach. All cells are cubic cells of equal volume $a^3$, with $a=1\left[\text{nm}\right]$; the polarization ${\vec{P}}_n$ is a one-component vector along the $x$ axis, i.e., ${\vec{P}}_n=\left(P_n,0,0\right)$, whereas the magnetization described by the spins ${\vec{S}}_{l,i}$ and the spins ${\vec{S}}_{r,j}$ are vectors that display three components, i.e., ${\vec{S}}_{l,i}=\left(S_{l,i}^x,S_{l,i}^y,S_{l,i}^z\right)$ and ${\vec{S}}_{r,j}=\left(S_{r,j}^x,S_{r,j}^y,S_{r,j}^z\right)$. We also consider that the polarization and the magnetization are orthogonal in the equilibrium configuration [19, 20]: ${\vec{P}}_n=\left(P,0,0\right), {\vec{S}}_{l,i}=(0,0,S)$, and ${\vec{S}}_{r,j}=(0,0,S)$. The indices $l$ and $r$ refer to the left and right FM components, whereas $n$ and $i$ or $j$ correspond to the site positions of the polarization and the spins in the MF material, respectively.

Figure 2

Modeling of a four-level MLC memory with a trilayers FM/FE/FM MF composite material: Simultaneous control of two magnetic bits by means of an electrical excitation. The electrical excitation, i.e., the excitation of the polarization, is done at the middle of the FE part of the MF material. The two bit states on(a)–(d) correspond to the wave number values $q=1, q=1.2, q=0.85$, and $q=3.1$, respectively. We set $A=2$ and $L=10/3$.

Figure 3

The 11, 10, and 01 two-bit state profiles at a time (a)–(c) before and (d)–(f) after the pinning of the solitary wave at the FM edges, and the 00 two-bit state profile at (g).

Figure 4

Modeling of an electromagnetic oscillator with a trilayer FM/FE/FM MF composite material. (a) or (b) display an electromagnetic oscillator in which the information is transformed alternately into an electrical signal and into a magnetic signal, during its propagation through the MF material. The excitation of the polarization that is responsible for these oscillations is done in the middle of the FE component. Its amplitude and its width are fixed to $A=0.7$ and $L=10/3$. For (a) the wave number is fixed to $q=5$ and for (b) it is fixed to $q=7.5$. (c) displays the evolution in a logic representation of the states of the electromagnetic oscillator displayed in (a) or (b). The magnetic alternations of the signal last twice as long as the electric alternations.